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Schrodingers Equation

1. Homework Statement
Show that the function [tex]\Psi(x,t)=Asin(kx- \omega t)[/tex] does not satisfy the time-independent Schrodinger Equation.


2. Homework Equations
Time independet SE



3. The Attempt at a Solution
I think i have to solve for derivative of [tex]\Psi(x,t)/t[/tex] and second derivative of [tex]\Psi(x,t)/x[/tex] but i'm not sure how to answer the question.

I attempted to differentiate the wave function with respect to time and space so that i got
[tex]\partial\Psi(x,t)/\partial t = -\omega Acos(kx-\omegat)[/tex]
and that [tex]\partial^2\Psi(x,t)/\partial x^x = -kAsin(kx-\omegat)[/tex]

If so, how do i prove that the original function does not satisfy the TDSE?
 
Last edited:
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The time-independent Schrödinger equation says Hψ = Eψ, where E is the eigenvalue. The Hamiltonian will tell you what to differentiate with respect to.
 

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